Minimizing sequences in optimal control with approximately given input data and the regularizing properties of the Pontryagin maximum principle

Results related to the optimal control theory for systems with approximately given input data are presented. The basic (desired) element in the theory is the minimizing sequence of feasible controls rather than the classical optimal control. Necessary and sufficient conditions for minimizing sequences are established. The regularizing properties of the Pontryagin maximum principle and of minimizing sequences are discussed. Three basic regularization levels are singled out that are characteristic of any optimal control problem. The stability of the optimal value in a problem depending on the constraint parameter is discussed. Illustrative examples are considered in detail.